The ρ ±−ρ 0 mass splitting problem

The problem of the ρ ^±−ρ ⁰mass splitting is discussed. It is suggested to use the φ→ρπ→3π decay to measure the ρ ^±−ρ ⁰ mass splitting. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 8–11 (10 January 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Ultrasonic wave propagation in concentrated slurries – The modelling problem

The suspended particle size distribution in slurries can, in principle, be estimated from measured ultrasonic wave attenuation across a frequency band in the 10s of MHz range. The procedure requires a computational model of wave propagation which incorporates scattering phenomena. These models fail at high particle concentrations due to hydrodynamic effects which they do not incorporate. This work seeks an effective viscosity and density for the medium surrounding the particles, which would enable the scattering model predictions to match experimental data for high solids loading. It is found that the required viscosity model has unphysical characteristics leading to the conclusion that a simple effective medium modification to the ECAH/LB is not possible. The paper confirms the successful results which can be obtained using core–shell scattering models, for smaller particles than had previously been studied, and outlines modifications to these which would permit rapid computation of sufficient stability to support fast particle sizing procedures.     

The Rubik’s cube problem revisited: a statistical thermodynamic approach

Inspired by the protein folding problem, we propose a Rubik’s cube model and study its thermodynamic and kinetic behavior. We find that the energy landscape contains a tiny funnel-like region, as the dynamics towards the native state is mostly diffusive. In particular, from Monte Carlo simulations we observe exponential kinetics in the first-passage-time distribution towards the native state at all temperatures considered, while the complexity of the energy landscape is exhibited through a stretched-exponential relaxation of the energy autocorrelation function. The rollover feature in the mean first passage time, as observed in many protein-folding dynamics studies, is captured again in our model and discussed under the statistical energy landscape approach.     

The equation-transform model for Dirac–Morse problem including Coulomb tensor interaction

The approximate solutions of Dirac equation with Morse potential in the presence of Coulomb-like tensor potential are obtained by using Laplace transform (LT) approach. The energy eigenvalue equation of the Dirac particles is found and some numerical results are obtained. By using convolution integral, the corresponding radial wave functions are presented in terms of confluent hypergeometric functions.     

The non-commutative oscillator, symmetry and the Landau problem

The isotropic oscillator on a plane is discussed where the coordinate and momentum space are both considered to be non-commutative. We also discuss the symmetry properties of the oscillator for three separate cases when the non-commutative parameters Θ and for x and p-space, respectively, satisfy specific relations. We compare the Landau problem with the isotropic oscillator on non-commutative space and obtain a relation between the two non-commutative parameters and the magnetic field of the Landau problem.     

On the ν-dimensional one-component classical plasma: The thermodynamic limit problem revisited

We prove theH-stability property and the existence of the thermodynamic limit of the free energy density of the two-dimensional, one-component classical plasma. We give lower and upper bounds on the free energy density in any dimensionv and draw some consequences.     

The enhanced volume source boundary point method for the calculation of acoustic radiation problem

The Volume Source Boundary Point Method(VSBPM) is greatly improved so that it will speed up the VSBPM‘s solution of the acoustic radiation problem caused by the vibrating body.The fundamental solution provided by Helmholtz equation is enforced in a weighted residual sense over a tetrahedron located on the normal line of the boundary node to replace the coefficient matrices of the system equation.Through the enhanced volume source boundary point analysis of various examples and the sound field of a vibrating rectangular box in a semi-anechoic chamber,it has revealed that the calculating speed of the EVSBPM is more than 10 times faster than that of the VSBPM while it workss on the aspects of its calculating precision and stability,adaptation to geometric shape of vibrating body as well as its ability to overcome the non-uniqueness problem.     

What is the problem in the locality problem?

In connection with my previous paper Locality, Reflection, and Wave-Particle Duality [Found. Phys. 17, 813 (1987)], in this paper I distinguish explicitly, in the locality problem, between assertions, deductively established results, interpretations, intuitions, and facts. This clarifies the structure of the problem.     

Generalized quantum mechanical two-Coulomb-center problem （Demkov problem）

We present a new exactly solvable quantum problem for which the Schro¨dinger equation allows for separation of variables in oblate spheroidal coordinates. Namely, this is the quantum mechanical two-Coulomb-center problem for the case of an imaginary intercenter parameter and complex conjugate charges are considered. Since the potential is defined by the two-sheeted mapping whose singularities are concentrated on a circle rather than at separate points, there arise additional possibilities in the choice of boundary conditions. A detailed classification of the various types of boundary-value problems is given. The quasi-radial equation leads to a new type of boundary value problem which has never been considered before. Results of the numerical calculations, which allow conclusions to be drawn about the structure of the energy spectrum, are shown. Possible physical applications are discussed.     

The problem of pseudoreplication in neuroscientific studies: is it affecting your analysis?

Background  

Pseudoreplication occurs when observations are not statistically independent, but treated as if they are. This can occur when there are multiple observations on the same subjects, when samples are nested or hierarchically organised, or when measurements are correlated in time or space. Analysis of such data without taking these dependencies into account can lead to meaningless results, and examples can easily be found in the neuroscience literature.     

The problem of determining short-range order parameters in interpreting a M?ssbauer spectrum

We develop a procedure to interpret the model M?ssbauer spectra (MS) of resonant nuclei in a two-component crystal with short-range order. The procedure is describable not only by pair correlations but also by multiparticle correlations of the atomic distribution. The results of the interpretation are used to find M?ssbauer parameters for subspectra and for certain correlation moments that describe the short-range order. The developed approach was used to interpret the actual spectra of ⁵⁷Fe in iron-chromium alloys.     

The Vaidya problem in conformally flat Stäckel spaces of type (1.1)

The problem of classification of conformally flat radiation spaces admitting full separation of variables in the Hamilton–Jacobi equation is considered. The Vaidya problem for conformally flat St?ckel spaces of type (1.1) has been solved; the metrics and the radiation have been found in explicit form. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 12–14, January, 2009.     

The Neumann solution of the multiple scattering problem in a plane-parallel medium—IIc. The specific intensity in a semi-infinite space

Using a new formulation of the resolvent function [Rutily and Bergeat JQSRT 38, 61 (1987)], we solve the Milne integral equation for the mean intensity in a semi-infinite plane-parallel atmosphere. The specific intensity is then derived at any optical depth. By expanding the intensity in power series in the albedo, we derive the corresponding intensities of a n-times scattered radiation field propagating in a half-space (n ⩾/ 1).     

The Lie–Poisson representation of the nonlinearized eigenvalue problem of the Kac–van Moerbeke hierarchy

The Kac–van Moerbeke hierarchy is studied by a 3×3 discrete eigenvalue problem and the corresponding nonlinearized one an integrable Poisson map with a Lie–Poisson structure is also presented. Moreover, the 2×2 nonlinearized eigenvalue problem associated with the Kac–van Moerbeke hierarchy is proved to be a reduction of the Poisson map on the leaves of the symplectic foliation.     

The notion of observable and the moment problem for $$*$$∗-algebras and their GNS representations

Letters in Mathematical Physics - We address some usually overlooked issues concerning the use of $$*$$-algebras in quantum theory and their physical interpretation. If $${\mathfrak {A}}$$ is a...     

The Riemann–Hilbert problem to coupled nonlinear Schrödinger equation: Long-time dynamics on the half-line

We derive the long-time asymptotics for the solution of initial-boundary value problem of coupled nonlinear Schrödinger equation whose Lax pair involves 3 × 3 matrix in present paper. Based on a nonlinear steepest descent analysis of an associated 3 × 3 matrix Riemann–Hilbert problem, we can give the precise asymptotic formulas for the solution of the coupled nonlinear Schrödinger equation on the half-line.     

Tracking problem under a time-varying topology

This paper studies the multi-agent tracking problem of a third-order maneuvering target under uncertain communication environments. Each tracking agent is assumed to be a third-order system and can only use its own and neighbors＇ position, velocity, and acceleration information to design its control input. In this work, the uncertain communication environments are modelled by a finite number of constant Laplacian matrices together with their corresponding scheduling functions. Sufficient conditions for the existence of a tracking strategy have been expressed in terms of the solvability of linear matrix inequalities. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed tracking strategy.